For ReLU networks with width at least two in input and hidden layers, an open set of parameters is identifiable, implying functional dimension equals parameter count minus hidden neurons.
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Copositive matrices with nondecreasing off-diagonal entries admit a PSD plus nonnegative decomposition, which implies exactness of a natural relaxation for separable quadratic optimization over the simplex.
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Most ReLU Networks Admit Identifiable Parameters
For ReLU networks with width at least two in input and hidden layers, an open set of parameters is identifiable, implying functional dimension equals parameter count minus hidden neurons.
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Copositive Matrices with Ordered Off-Diagonal Entries
Copositive matrices with nondecreasing off-diagonal entries admit a PSD plus nonnegative decomposition, which implies exactness of a natural relaxation for separable quadratic optimization over the simplex.